The former Espanyol man, who scored against the Swans in a friendly in 2008, is thought to be in talks with chairman Huw Jenkins over a move to south west Wales.
Jenkins flew to Barcelona yesterday to speak with the representative of an unnamed player, who is high on boss Brendan Rodgers' summer wish list.
"I will be meeting with the representative of a player that we feel will be perfect for Swansea City," the Swans chairman told the official site.
"He has the talent that would fit in to the style in which we believe in, and we are hopeful of him coming here.
"By flying out to meet his representative, I hope we can agree a deal within the next few days. We will talk about what we want to achieve as a club, and what the player wishes to achieve too.
"After the arrival of Danny Graham and the recent news regarding Steven Caulker – along with Angel Rangel committing his future to the club – this would add to the feelgood factor around the club.
"We are determined to continue the good work put in over the last few years, and we will do it the way which is best for Swansea City."
Soriano is one of the most potent strikers outside the Spanish top flight after netting 31 goals in just 34 starts for Barcelona's B team, who play in Liga Adelante – the second tier of football in Spain.
He was thought to be on the way to Udinese as part of a part-exchange deal which would take Alexis Sanchez to the Nou Camp in a big money deal, but that move looks to have stalled.
Should Soriano sign, it would be the 3rd summer signing following the acquisitions of Danny Graham and Steven Caulker.